daviddoji/Kalman-and-Bayesian-Filters-in-Python
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in equations that update a variable using its previous value use different symbols (written as pseudocode it would be ok, but not written as an equation)

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Kloppenburg Ernst (CR/PJ-AI-R4) 2018-01-25 08:09:16 +01:00
parent a87766a898
commit 0a9fd12682
1 changed files with 8 additions and 8 deletions
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10-Unscented-Kalman-Filter.ipynb
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@ -378,8 +378,8 @@
"\n",
"through the nonlinear system:\n",
"\n",
"$$\\begin{cases}\\begin{aligned}x&=x+y\\\\\n",
"y &= 0.1x^2 + y^2\\end{aligned} \\end{cases}$$ "
"$$\\begin{cases}\\begin{aligned}\\bar x&=x+y\\\\\n",
"\\bar y&= 0.1x^2 + y^2\\end{aligned} \\end{cases}$$ "
]
},
{
@ -2773,17 +2773,17 @@
"\n",
"After the move forward for time $\\Delta t$ the new position and orientation of the robot is\n",
"\n",
"$$\\begin{aligned} x &= C_x + R\\sin(\\theta + \\beta) \\\\\n",
"y &= C_y - R\\cos(\\theta + \\beta) \\\\\n",
"\\theta &= \\theta + \\beta\n",
"$$\\begin{aligned} \\bar x &= C_x + R\\sin(\\theta + \\beta) \\\\\n",
"\\bar y &= C_y - R\\cos(\\theta + \\beta) \\\\\n",
"\\bar \\theta &= \\theta + \\beta\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"Once we substitute in for $C$ we get\n",
"\n",
"$$\\begin{aligned} x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
"y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
"\\theta &= \\theta + \\beta\n",
"$$\\begin{aligned} \\bar x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
"\\bar y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
"\\bar \\theta &= \\theta + \\beta\n",
"\\end{aligned}\n",
"$$\n",
"\n",